The Wikipedia article about primality tests seems fairly well written as an introduction, and has pointers to more complete resources. Just bear in mind that generating all primes up to some number and verifying whether a single number is prime or not are distinct problems, albeit related. Naive ideas connecting them are intuitive and immediate, but differences become relevant if computational complexity is to be taken into account. Indeed given that good old Sieve of Erathostenes is a good starting point, I was about to mention the quadratic sieve algorithm I had heard talking about, but a quick check revealed that it solves yet another (related, but more complex) problem, namely that of factorization.

To bring the subject back on (Perl) topic, although in a funny manner, I take the liberty to quote Abigail's

perl -le 'print "PRIME" if (1 x shift) !~ /^(11+)\1+$/' $number
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